Compression and Comprehension
It is a truth universally acknowledged, that a mind which beholds an emergence of exogenous order, must be in search of an underlying structure.
The Descartography of Mythopoesis: The Simulation Theory of Stories:
What this calls for is an investigation into the nature of truth. Which I think I'll leave for my next post. "But Fance, didn't you already do that in your theory of knowledge?" Yes, but this is different. Because instead of investigating the nature of truth as it logically relates to knowledge, we'll be investigating truth as it pragmatically relates to utility.
Oops. I lied. In writing the post about truth and utility, I realized I first need a to explain another corner of my worldview, and that it probably deserves a separate explanation. Which is going to be difficult, since I don’t know how to describe this exactly. Alas, it’s a load-bearing construct. Thus, a short detour.
I. The Unreasonable Effectiveness of Compression
There exists a pattern which which goes by many names: “sameness”; “equality”; “equivalence”; “symmetry”; “isomorphism”; “loops”; “repetition”; “recursion”; “parity”. Though the one I think I like the most, is invariance. I think it could reasonably be called “the mother of all patterns”. Because it’s contained within everything else that has any kind of orderly structure. And as a consequence, all useful knowledge relies on finding the similarities within that orderly structure, and then compressing it by squeezing out the similarities. It’s useful because the sameness allows our brains to compress the sameness of the multiplicity into a single numerical entity.
If we take numbers for example. What do integers represent, if not the sameness between instances of elements of a set? In Peano Arithmetic, 3 is defined as S(S(S(0))), where 0 is the identity element and S() is the successor function. And numbers in general are useful because they represent bijection between the number and the (possibly tangible) objects they represent. The concept of sameness shows up in both the successor function and the bijection.
At every hierarchy of abstraction, there's some sort of compression going on. If we look at real analysis for example, the hierarchy looks something like:
objects -> numberline -> arithmetic -> algebra -> calculus -> diff_eq/linear_algebra -> category theory
Likewise, consider writing. To experience an event first had offers a deluge of sensory perceptions. To write about such an experience, necessarily compresses it down to a few lines of text. The compression is very lossy. I.e. quite a few details get left out. Though hopefully, enough information is transmitted to reconstruct the most important details.
Consider a painting. Lots of people say art is supposed to be beautiful. But this doesn’t explain art which is ugly or grotesque. I think it’s more accurate to say that art is art to the extent that it compresses information. The denser the information, the deeper the meaning.
Compression is quite useful because minds do not have infinite storage space. For intelligence to exist, i.e. the universe must to some extent be compressible. The compressibility is what makes it potentially comprehensible to us mere mortals. To us bags of meat. One can perhaps imagine a lovecraftian universe where nothing makes sense, because the universe’s patterns are too complex to fit within its residents’ brains. And so the organisms act wormlike, thrashing about at random.
Because invariance is seemingly at the root of so many fields and disciplines, I liken it to the root of the tree of knowledge. Or alternatively, the root directory.
II. Keepin It Real
One of the ramifications of this perspective, is that it provides a tentative answer to the question of defining “reality”. I.e. reality, is that which is invariant under shifts in perspective.
One way to understand a concept is the contrast it with its opposite. What’s the opposite of reality? One possible answer is that the opposite of “reality” is “illusion”. And what is the essential nature of an illusion? I would say, that an illusion has the appearance of one scenario, but leads to different consequences than is implied by appearances.
E.g. suppose you're stranded in the desert and you think you see an oasis in the distance. Maybe it's a real oasis. Maybe it's a mirage. How do you tell? Well, the simplest way is to get closer to the phenomenon. If it's real, the oasis will continue to exist as you draw closer. You'll be able to drink and bath in it. If it's a mirage, the oasis will seemingly melt into the ground, and all that will be left is the barren desert.
In other words, we're always trying to figure out what's "real" and what's "fake” by probing reality from different perspectives. What this shows, is that the very idea of "reality" is itself a sort of abstraction. None of us have direct access to the noumena of the world. We are mere brains in a vat (and that vat is our cranium). All we can do is infer reality from the phenomena that our senses relay to us.